serket 0.0.9

We will use tensorflow datasets for dataloading. for more on interface of jax/tensorflow dataset see here

# imports
import tensorflow as tf
# Ensure TF does not see GPU and grab all GPU memory.
tf.config.set_visible_devices([], device_type="GPU")
import tensorflow_datasets as tfds
import tensorflow.experimental.numpy as tnp
import jax
import jax.numpy as jnp
import jax.random as jr 
import optax  # for gradient optimization
import serket as sk
import matplotlib.pyplot as plt
import functools as ft

# Construct a tf.data.Dataset
batch_size = 128

# convert the samples from integers to floating-point numbers
# and channel first format
def preprocess_data(x):
    # convert to channel first format
    image = tnp.moveaxis(x["image"], -1, 0)
    # normalize to [0, 1]
    image = tf.cast(image, tf.float32) / 255.0

    # one-hot encode the labels
    label = tf.one_hot(x["label"], 10) / 1.0
    return {"image": image, "label": label}


ds_train, ds_test = tfds.load("mnist", split=["train", "test"], shuffle_files=True)
# (batches, batch_size, 1, 28, 28)
ds_train = ds_train.shuffle(1024).map(preprocess_data).batch(batch_size).prefetch(tf.data.AUTOTUNE)

# (batches, 1, 28, 28)
ds_test = ds_test.map(preprocess_data).prefetch(tf.data.AUTOTUNE)

🏗️ Model definition

We will use jax.vmap(model) to apply model on batches.

@sk.treeclass
class CNN:
    def __init__(self):
        self.conv1 = sk.nn.Conv2D(1, 32, (3, 3), padding="valid")
        self.relu1 = sk.nn.ReLU()
        self.pool1 = sk.nn.MaxPool2D((2, 2), strides=(2, 2))
        self.conv2 = sk.nn.Conv2D(32, 64, (3, 3), padding="valid")
        self.relu2 = sk.nn.ReLU()
        self.pool2 = sk.nn.MaxPool2D((2, 2), strides=(2, 2))
        self.flatten = sk.nn.Flatten(start_dim=0)
        self.dropout = sk.nn.Dropout(0.5)
        self.linear = sk.nn.Linear(5*5*64, 10)

    def __call__(self, x):
        x = self.conv1(x)
        x = self.relu1(x)
        x = self.pool1(x)
        x = self.conv2(x)
        x = self.relu2(x)
        x = self.pool2(x)
        x = self.flatten(x)
        x = self.dropout(x)
        x = self.linear(x)
        return x

model = CNN()

🎨 Visualize model

print(model.summary(show_config=False, array=jnp.empty((1, 28, 28))))  
┌───────┬─────────┬─────────┬──────────────┬─────────────┬─────────────┐
│Name   │Type     │Param #  │Size          │Input        │Output       │
├───────┼─────────┼─────────┼──────────────┼─────────────┼─────────────┤
│conv1  │Conv2D   │320(0)   │1.25KB(0.00B) │f32[1,28,28] │f32[32,26,26]│
├───────┼─────────┼─────────┼──────────────┼─────────────┼─────────────┤
│relu1  │ReLU     │0(0)     │0.00B(0.00B)  │f32[32,26,26]│f32[32,26,26]│
├───────┼─────────┼─────────┼──────────────┼─────────────┼─────────────┤
│pool1  │MaxPool2D│0(0)     │0.00B(0.00B)  │f32[32,26,26]│f32[32,13,13]│
├───────┼─────────┼─────────┼──────────────┼─────────────┼─────────────┤
│conv2  │Conv2D   │18,496(0)│72.25KB(0.00B)│f32[32,13,13]│f32[64,11,11]│
├───────┼─────────┼─────────┼──────────────┼─────────────┼─────────────┤
│relu2  │ReLU     │0(0)     │0.00B(0.00B)  │f32[64,11,11]│f32[64,11,11]│
├───────┼─────────┼─────────┼──────────────┼─────────────┼─────────────┤
│pool2  │MaxPool2D│0(0)     │0.00B(0.00B)  │f32[64,11,11]│f32[64,5,5]  │
├───────┼─────────┼─────────┼──────────────┼─────────────┼─────────────┤
│flatten│Flatten  │0(0)     │0.00B(0.00B)  │f32[64,5,5]  │f32[1600]    │
├───────┼─────────┼─────────┼──────────────┼─────────────┼─────────────┤
│dropout│Dropout  │0(0)     │0.00B(0.00B)  │f32[1600]    │f32[1600]    │
├───────┼─────────┼─────────┼──────────────┼─────────────┼─────────────┤
│linear │Linear   │16,010(0)│62.54KB(0.00B)│f32[1600]    │f32[10]      │
└───────┴─────────┴─────────┴──────────────┴─────────────┴─────────────┘
Total count :	34,826(0)
Dynamic count :	34,826(0)
Frozen count :	0(0)
------------------------------------------------------------------------
Total size :	136.04KB(0.00B)
Dynamic size :	136.04KB(0.00B)
Frozen size :	0.00B(0.00B)
========================================================================

print(model.tree_diagram())
CNN
    ├── conv1=Conv2D
    │   ├── weight=f32[32,1,3,3]
    │   ├── bias=f32[32,1,1]
    │   ├*─ in_features=1
    │   ├*─ out_features=32
    │   ├*─ kernel_size=(3, 3)
    │   ├*─ strides=(1, 1)
    │   ├*─ padding=((0, 0), (0, 0))
    │   ├*─ input_dilation=(1, 1)
    │   ├*─ kernel_dilation=(1, 1)
    │   ├── weight_init_func=Partial(init(key,shape,dtype))
    │   ├── bias_init_func=Partial(zeros(key,shape,dtype))
    │   └*─ groups=1    
    ├── relu1=ReLU  
    ├*─ pool1=MaxPool2D
    │   ├*─ kernel_size=(2, 2)
    │   ├*─ strides=(2, 2)
    │   └*─ padding='valid' 
    ├── conv2=Conv2D
    │   ├── weight=f32[64,32,3,3]
    │   ├── bias=f32[64,1,1]
    │   ├*─ in_features=32
    │   ├*─ out_features=64
    │   ├*─ kernel_size=(3, 3)
    │   ├*─ strides=(1, 1)
    │   ├*─ padding=((0, 0), (0, 0))
    │   ├*─ input_dilation=(1, 1)
    │   ├*─ kernel_dilation=(1, 1)
    │   ├── weight_init_func=Partial(init(key,shape,dtype))
    │   ├── bias_init_func=Partial(zeros(key,shape,dtype))
    │   └*─ groups=1    
    ├── relu2=ReLU  
    ├*─ pool2=MaxPool2D
    │   ├*─ kernel_size=(2, 2)
    │   ├*─ strides=(2, 2)
    │   └*─ padding='valid' 
    ├*─ flatten=Flatten
    │   ├*─ start_dim=0
    │   └*─ end_dim=-1  
    ├── dropout=Dropout
    │   ├*─ p=0.5
    │   └── eval=None   
    └── linear=Linear
        ├── weight=f32[1600,10]
        ├── bias=f32[10]
        ├*─ in_features=1600
        └*─ out_features=10  
    

 
# set all dropout off
test_model = model.at[model == "eval"].set(True, is_leaf=lambda x: x is None)

def show_images_with_predictions(model, images, one_hot_labels):
    logits = jax.vmap(model)(images)
    predictions = jnp.argmax(logits, axis=-1)
    fig, axes = plt.subplots(5, 5, figsize=(10, 10))
    for i, ax in enumerate(axes.flat):
        ax.imshow(images[i].reshape(28, 28), cmap="binary")
        ax.set(title=f"Prediction: {predictions[i]}\nLabel: {jnp.argmax(one_hot_labels[i], axis=-1)}")
        ax.set_xticks([])
        ax.set_yticks([])
    plt.show()

example = ds_test.take(25).as_numpy_iterator()
example = list(example)
sample_test_images = jnp.stack([x["image"] for x in example])
sample_test_labels = jnp.stack([x["label"] for x in example])

show_images_with_predictions(test_model, sample_test_images, sample_test_labels)

🏃 Train the model

@ft.partial(jax.value_and_grad, has_aux=True)
def loss_func(model, batched_images, batched_one_hot_labels):
    logits = jax.vmap(model)(batched_images)
    loss = jnp.mean(optax.softmax_cross_entropy(logits=logits, labels=batched_one_hot_labels))
    return loss, logits


# using optax for gradient updates
optim = optax.adam(1e-3)
optim_state = optim.init(model)


@jax.jit
def batch_step(model, batched_images, batched_one_hot_labels, optim_state):
    (loss, logits), grads = loss_func(model, batched_images, batched_one_hot_labels)
    updates, optim_state = optim.update(grads, optim_state)
    model = optax.apply_updates(model, updates)
    accuracy = jnp.mean(jnp.argmax(logits, axis=-1) == jnp.argmax(batched_one_hot_labels, axis=-1))
    return model, optim_state, loss, accuracy


epochs = 5

for i in range(epochs):
    epoch_accuracy = []
    epoch_loss = []

    for example in ds_train.as_numpy_iterator():
        image, label = example["image"], example["label"]
        model, optim_state, loss, accuracy = batch_step(model, image, label, optim_state)
        epoch_accuracy.append(accuracy)
        epoch_loss.append(loss)

    epoch_loss = jnp.mean(jnp.array(epoch_loss))
    epoch_accuracy = jnp.mean(jnp.array(epoch_accuracy))

    print(f"epoch:{i+1:00d}\tloss:{epoch_loss:.4f}\taccuracy:{epoch_accuracy:.4f}")
    
# epoch:1	loss:0.2706	accuracy:0.9268
# epoch:2	loss:0.0725	accuracy:0.9784
# epoch:3	loss:0.0533	accuracy:0.9836
# epoch:4	loss:0.0442	accuracy:0.9868
# epoch:5	loss:0.0368	accuracy:0.9889

🎨 Visualize After training

test_model = model.at[model == "eval"].set(True, is_leaf=lambda x: x is None)
show_images_with_predictions(test_model, sample_test_images, sample_test_labels)

We will try to estimate NN(x)~f(x), where df(x)/dx = cos(x) and df(x)/dx will be represented with finite difference scheme

import copy

import jax
import jax.numpy as jnp
import matplotlib.pyplot as plt
import optax

import serket as sk

x = jnp.linspace(-jnp.pi, jnp.pi, 1000)[:, None]
y = jnp.sin(x)
dx = x[1] - x[0]
dydx = jnp.cos(x)

NN_fd = sk.nn.Sequential(
    [
        sk.nn.Linear(1, 128),
        sk.nn.ReLU(),
        sk.nn.Linear(128, 128),
        sk.nn.ReLU(),
        sk.nn.Linear(128, 1),
    ]
)

NN_ad = copy.copy(NN_fd)
optim = optax.adam(1e-3)


@jax.value_and_grad
def loss_func_fd(NN, x):
    y = NN(x)
    dydx = sk.fd.difference(y, axis=0, accuracy=5, step_size=dx)
    loss = jnp.mean((dydx - jnp.cos(x)) ** 2)
    loss += jnp.mean((NN(jnp.zeros_like(x))) ** 2)  # initial condition
    return loss


@jax.value_and_grad
def loss_func_ad(NN, x):
    loss = jnp.mean((sk.diff(NN)(x) - jnp.cos(x)) ** 2)
    loss += jnp.mean(NN(jnp.zeros_like(x)) ** 2)  # initial condition
    return loss


@jax.jit
def step_fd(NN, x, optim_state):
    loss, grads = loss_func_fd(NN, x)
    updates, optim_state = optim.update(grads, optim_state)
    NN = optax.apply_updates(NN, updates)
    return NN, optim_state, loss


def train_fd(NN_fd, optim_state_fd, epochs):
    for i in range(1, epochs + 1):
        NN_fd, optim_state_fd, loss_fd = step_fd(NN_fd, x, optim_state_fd)
    return NN_fd, optim_state_fd, loss_fd


@jax.jit
def step_ad(NN, x, optim_state):
    loss, grads = loss_func_ad(NN, x)
    updates, optim_state = optim.update(grads, optim_state)
    NN = optax.apply_updates(NN, updates)
    return NN, optim_state, loss


def train_ad(NN_ad, optim_state_ad, epochs):
    for i in range(1, epochs + 1):
        NN_ad, optim_state_ad, loss_ad = step_ad(NN_ad, x, optim_state_ad)
    return NN_ad, optim_state_ad, loss_ad


epochs = 1000


optim_state_fd = optim.init(NN_fd)
optim_state_ad = optim.init(NN_ad)


NN_fd, optim_state_fd, loss_fd = train_fd(NN_fd, optim_state_fd, epochs)
NN_ad, optim_state_ad, loss_ad = train_ad(NN_ad, optim_state_ad, epochs)
print(f"Loss_fd {loss_fd:.4f} \nLoss_ad {loss_ad:.4f}")
y_fd = NN_fd(x)
y_ad = NN_ad(x)
plt.plot(x, y, "--k", label="true")
plt.plot(x, y_fd, label="fd pred")
plt.plot(x, y_ad, label="ad pred")
plt.legend()

# Loss_fd 0.0012 
# Loss_ad 0.0235

import jax
import jax.numpy as jnp
import matplotlib.pyplot as plt
import optax

import serket as sk

x, y = [jnp.linspace(-1, 1,50)] * 2
dx, dy = [x[1] - x[0]] * 2
X, Y = jnp.meshgrid(x, y, indexing="ij")

F1 = -Y
F2 = +X
F = jnp.stack([F1, F2], axis=0)

NN = sk.nn.Sequential(
    [
        sk.nn.Conv2D(2, 32, kernel_size=3, padding="same"),
        sk.nn.ReLU(),
        sk.nn.Conv2D(32, 32, kernel_size=3, padding="same"),
        sk.nn.ReLU(),
        sk.nn.Conv2D(32, 2, kernel_size=3, padding="same"),
    ]
)

optim = optax.adam(1e-3)


@jax.value_and_grad
def loss_func(NN, F):
    F_pred = NN(F)
    div = sk.fd.divergence(F_pred, accuracy=5, step_size=(dx, dy))  
    loss = jnp.mean(div**2)  # divergence free condition
    curl = sk.fd.curl(F_pred, accuracy=2, step_size=(dx, dy))
    loss += jnp.mean((curl-jnp.ones_like(curl)*2)**2)  # curl condition 
    return loss


@jax.jit
def step(NN, F, optim_state):
    loss, grads = loss_func(NN, F)
    updates, optim_state = optim.update(grads, optim_state)
    NN = optax.apply_updates(NN, updates)
    return NN, optim_state, loss


def train(NN, Z, optim_state, epochs):
    for i in range(1, epochs + 1):
        NN, optim_state, loss = step(NN, Z, optim_state)
    return NN, optim_state, loss


Z = jnp.stack([X, Y], axis=0)  # collocation points
optim_state = optim.init(NN)  # initialise optimiser
epochs = 1_000
NN, _, loss = train(NN, Z, optim_state, epochs)

Fpred = NN(Z)  # predicted field

plt.figure(figsize=(10, 10))
plt.quiver(X, Y, Fpred[0], Fpred[1], color="r", label="pred")
plt.quiver(X, Y, F1, F2, color="k", alpha=0.5, label="true")
plt.legend()